Hybrid scheduling for the parallel solution of linear systems

Abstract

In this paper, we consider the problem of designing a dynamic scheduling strategy that takes into account both workload and memory information in the context of the parallel multifrontal factorization. The originality of our approach is that we base our estimations (work and memory) on a static optimistic scenario during the analysis phase. This scenario is then used during the factorization phase to constrain the dynamic decisions. The task scheduler has been redesigned to take into account these new features. Moreover performance have been improved because the new constraints allow the new scheduler to make optimal decisions that were forbidden or too dangerous in unconstrained formulations. Performance analysis show that the memory estimation becomes much closer to the memory effectively used and that even in a constrained memory environment we decrease the factorization time with respect to the initial approach.Key-words: sparse matrices, parallel multifrontal method, dynamic scheduling, memory.This text is also available as a research report of the Laboratoire de l'Informatique du Parallélisme http://www.ens-lyon.fr/LIP and as a technical report from ENSEEIHT-IRIT. Stratégies d'ordonnancement hybrides pour la résolution parallèle de systèmes linéairesRésumé : Nous proposons des stratégies d'ordonnancement bi-critères, qui s'inté-ressentà la foisà la performance età la consommation mémoire d'un algorithme parallèle de factorisation de matrices creuses, basé sur la méthode multifrontale. L'originalité de notre approche est que nous basons nos estimations mémoire sur un scénario optimiste (simulation lors de la phase d'analyse), qui est ensuite utilisé lors de la factorisation pour contraindre les décisions dynamiques d'ordonnancement. Un nouvel ordonnanceur aété implanté, qui prend en compte ces nouvelles contraintes. De plus, la performance aété améliorée parce que notre nouvelle approche permet a l'ordonnanceur de prendre des décisions meilleures, quiétaient interdites ou trop dangereuses auparavant. Une analyse de performance montre que les estimations mémoire sont beaucoup plus proches de la mémoire effectivement utilisée, et que le temps de factorisation est amélioré de façon significative par rapportà l'approche initiale.

Advances in the simulation of viscoplastic fluid flows using interior-point methods

“…Thanks to the flexibility offered by FEniCS in the choice of the linear system solver, we used the direct solver MUMPS [33,34] which enables to solve large sparse linear systems. Computations have been realized on a Intel Core i7-4600U (2.1 GHz).…”

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“…Work is currently in progress to implement this solver. As an alternative, ISSM uses the Multifrontal Massively Parallel Sparse direct solver (MUMPS) [Amestoy et al, 2001[Amestoy et al, , 2006. Although poorly scalable, this solver does not suffer from convergence issues, as it relies on a direct solving method.…”

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“…Pardiso [6,18], MUMPS [7,19], and SuperLU8 belong to direct methods. Though the direct methods are quite efficient for rmany applications, they might still be quite costly when matrixes are very large.…”

“…In the other kind, we could also classify the methods into two groups: direct solvers and iterative solvers. Pardiso [6], MUMPS [7], and SuperLU [8] belong to the direct methods. Conjugate gradient [9], multigrid method [10], and streaming multigrid solver [11] are the commonly used iterative solvers.…”